Question

Write the rational number \[\dfrac{{329}}{{400}}\] in decimal form. Also, find the kind of decimal expansion.

Answer 1

Hint: This question involves the arithmetic operations like addition/ subtraction/ multiplication/ division. We need to know the relation between rational numbers and decimal numbers. We need to know how to find the greatest common factor between two terms to make an easy calculation for these types of questions.

Complete step-by-step answer:
In this question, we would convert \[\dfrac{{329}}{{400}}\] it into its decimal form.
We know that the rational number means it has a numerator and denominator term, the decimal number is which has a decimal point with that.
We have \[\dfrac{{329}}{{400}} = ?\]
Here, we have \[329\] . \[329\] Is lesser than \[400\] . So, we put a decimal point and drop one zero.
So, we get \[3290\] . We know that \[400 \times 8 = 3200\] .
So, we put \[8\] in the quotient. By subtracting \[3290\] and \[3200\], we get \[90\] .
On further simplifying, we have \[90\] .
\[90\] Is lesser than \[400\] . So, we drop one zero. We can take zero because we have a decimal point. So, we have \[900\] .
We know that \[400 \times 2 = 800\] .
So, we put \[2\] in the quotient. By subtracting \[900\] and \[800\], we get \[100\] .
On further simplification, we have \[100\] .
\[100\] Is lesser than \[400\] . So, we drop another one zero. So, we get \[1000\] .
We know that \[2 \times 400 = 800\] . So, we put \[2\] in the quotient. By subtract \[1000\] and \[800\], we get \[200\]
And, we have \[200\] .
\[200\] Is lesser than \[400\] . So, we drop one zero. So, we get \[2000\] .
We know that \[400 \times 5\] \[ = 2000\] .so, we put \[5\] in the quotient. By subtracting \[2000\] and \[2000\] we get zero.
In step \[5\], we have the remainder as zero.
By using this normal division process we get,
 \[\dfrac{{329}}{{400}} = 0.8225\]
So, the final answer is,
 \[\dfrac{{329}}{{400}} = 0.8225\], it is terminating decimal.

Note: This question describes the arithmetic operations like addition/ subtraction/ multiplication/ division. Note that in the normal division process by including decimal points in the quotient we can include an extra zero in the dividend to make the easy calculation. Also, note that if the division process is continued more than seven five steps we can take only three-digit after the decimal point as the final answer.